Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector equation r = t < 2.5, 1.5, 0.5 >. What is the equation of the line?   Please explain your steps and show work.

Q: Find the equation of the plane that is parallel to the vectors (1,0,1) and (0,1,1), passing through…

A:

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

A:

Q: Find the equation of the plane that is parallel to the vectors (1,0,2) and (0,1,1), passing through…

A: Sol Given                   Parallel to the vectors  &lt;0,1,2&gt; &amp;&lt; 0,1,1&gt;…

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

A:

Q: Verify that it’s possible for a line with direction vector   d=(2,1,-2) to lie flat on a plane with…

A:

Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

A:

Q: 3. Find a vector equation for the line through (2, 7, −3) that is orthogonal to the plane 3x + y −4z…

A:

Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

A:

Q: 10

A:

Q: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=&lt;-1,4,2&gt;   To Find : Equation of the plane that…

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of plane

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: The plane contains the point (2, −1, 6) and is normal to the vector &lt;2, −1, 6&gt;.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A: NOTE: Refresh your page if you can't see any equations. . The normal vector is  and the given point…

Q: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

A:

Q: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1).…

A:

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

A:

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: Find the equation of the plane that is parallel to the vectors (3,0,2) and (0,1,2), passing through…

A:

Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Find the vector equation of the line (a) through the point (1, −5) and parallel to the x-axis; (b)…

A: As per our guideline we are allowed to do 1 question and 3 subparts at a time. Please post other…

Q: Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a…

A: Plane passing through the point P-1, 1, 0 and has a normal vector n=2, 0, -4.

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

A:

Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

A:

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the linear equation of the plane through the point(1,2,3) and contains the line represented by…

A:

Q: 5) Verify that it's possible for a line with direction vector d = (2,1,- 2) to lie flat on a plane…

A: For the vector representation of a plane , the vectors and lie on the plane. For the equation of…

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: 4. Find the equation of the plane containing the point (2, 7, −3) that is orthogonal to the line…

A:

Q: Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane containing…

A: Given problem:- Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the…

Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

A:

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

A:

Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector &lt;a, b, c&gt; is: ax+by+cz+d=0 Therefore,…

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.